Question

Code.
-3x + 4y = -8
8x - y = 16
Solving systems by substitution

Answer 1

The solution to the system of equations is
`\displaystyle \big((56)/(29), -(16)/(29)\big)`.

Explanation:

We are given a system of equations:

`\displaystyle \left \{ {{-3x+4y=-8} \atop {8x-y=16}} \right.`

• We need to solve these by substitution, so we need to solve one equation for a variable and then substitute the value of that variable into the other equation.
• After doing this and solving for the opposite variable, we need to insert this into the original equation and solve for the initial variable.
• Therefore, to solve one of the equations, we will solve it to put it in slope-intercept form and solve for y. The easier equation to work with is equation two.

`\displaystyle 8x - y = 16\\\\-y = -8x + 16\\\\(-y)/(-1)=(-8x+16)/(-1)\\\\y = 8x - 16`

Now, we've solved for y. So, we can substitute this into either equation and solve for x.

`\displaystyle -3x + 4(8x -16)=-8\\\\-3x + 32x - 64 = -8\\\\29x - 64 = -8\\\\29x = 56\\\\(29x)/(29)=(56)/(29)\\\\x = (56)/(29)`

Now, we substitute our value for x into one of the original equations and solve for y.

`\displaystyle 8\big((56)/(29)\big)-y=16\\\\-y = 16 - 8\big((56)/(29)\big)\\\\-y=(16)/(29)\\\\(-y)/(-1)=((16)/(29))/(-1)\\\\y = -(16)/(29)`

Therefore, the solution to our system of equations is:

• 
  `\displaystyle \big((56)/(29), -(16)/(29)\big)`